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iragen [17]
3 years ago
7

The probability that a student is accepted to a prestigious college is 0.3. If 5 students from the same school apply, what is th

e probability that at most 4 are accepted
Mathematics
1 answer:
hodyreva [135]3 years ago
6 0

Answer:0.849185

Step-by-step explanation:

Binomial probability formula we will use:

$P(x)=\frac{n !}{x !(n-x) !} p^{x} q^{n-x}$

where,

n=5$\\$\mathrm{P}$ (probability of success) $=0.3$\\q=1-p

The computation of the probability will be :

$P(x \leq 2 ; 5,0.3)=P(x=0 ; 5,0.3)+P(x=1 ; 5,0.3)+P(x=2 ; 5,0.3)+P(x=3 ; 5,0.3)$\\$=\left[\frac{5 !}{5 !(5-0) !}(0.3)^{0}(1-0.3)^{5-0}\right]+\left[\frac{5 !}{5 !(5-1) !}(0.3)^{1}(1-0.3)^{5-1}\right]$$+\left[\frac{5 !}{5 !(5-2) !}(0.3)^{2}(1-0.3)^{5-2}\right]$$++\left[\frac{5 !}{5 !(5-3) !}(0.3)^{3}(1-0.3)^{5-3}\right]$$++\left[\frac{5 !}{5 !(5-4) !}(0.3)^{4}(1-0.3)^{5-4}\right]$\\$=0.1681+0.3601+0.3087+0.006615+0.00567$\\$\Rightarrow 0.849185$

The probability that at most 4 are accepted = 0.849185

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